轴力及双向弯矩下钢筋混凝土截面新型快速应力积分算法

A NEW FAST STRESS INTEGRATION ALGORITHM FOR REINFORCED CONCRETE SECTIONS UNDER AXIAL FORCE AND BIAXIAL BENDING

轴力和双向弯矩作用下钢筋混凝土构件正截面极限承载力分析需要通过迭代调整截面中性轴的位置和方向以使截面应力积分与给定的外荷载满足平衡条件。为提高截面应力积分的计算效率和求解精度,提出了一种新型快速应力积分算法。考虑到混凝土应力-应变曲线为分段函数的特点,该方法基于迭代步中的应变分布将截面单元分解为多个积分子域,并通过二次等参映射和高斯数值积分方法对各子域进行应力积分。该方法在迭代过程中无需对初始网格信息做任何修改,可适用于任意形状的钢筋混凝土构件正截面极限承载力分析。通过算例分析,考察了方法的计算效率和有效性。

To evaluate the ultimate strength capacity of reinforced concrete sections subjected to combined axial force and biaxial bending, the equilibrium equations between the external forces and stress integration over the section shall be satisfied by modifying the depth and the inclination angle of the neutral axis via iteration process. To improve the efficiency and accuracy of stress integration over cross section, a new fast stress integration algorithm is proposed. In consideration of the stress field to be integrated is defined as a step function, according to the strain distribution across the section, firstly the integration area is decomposed into quadrilateral elements, which shall be further refined into several triangular or quadrangular subdomains; then, the stress integration in each quadrilateral element is performed using Gauss quadrature and second-order iso-parametric mapping method. With the proposed method, calculation can be performed without any modification for original meshes in the iteration process. It is suitable for any arbitrary-shaped cross section, including circular sections or multi-cellular hollow sections. The numerical performance of the algorithm has been extensively validated for a wide range of reinforced concrete sections.